The era of Antiquity can be seen as the era of calculator
devices that had no memory, no means to output the results other then
dials or indicators. In this period science became less demonized
and more widely accepted for what it was: science. No one was sent
to the burn stake anymore and not all magic was Satan's work anymore.
Though in rural areas the superstition was kept well alive by the
clerics until far into the 19th century. Also economic factors
played a role in the acceptance of pure science and discoveries made
from the practice of science.

New forms of mathematics were developed like the binary calculus.
The first automata appeared in the royal courts as some kind of miracle
machines. Remember when we wrote about the first oracles with hidden
people in the statues? Some miracle automata where still hiding small
people.

1672

Gottfried Wilhelm von Leibnitz (1646-1716 Germany)
a mathematician, physicist, philosopher, theologian, historian and inventor,
start to develop a calculator that will be the next generation of the
Pascaline, the machine becomes available in 1694.(12)

Leibnitz realizes that the weakness of the
Pascaline laid in the multiplication and division. And also that a commercial
successful machine should be working on a different principle. He adds
a gear with nine teeth of different length providing a mechanism to his
machine what could divide and multiply.
This is a prime example of how reckoners or other machines like calculating
devices are improved upon by different people. Leibnitz designs the machine
on the principle, or purpose, to mechanize the calculations on trigonometric
and astronomical tables. The same principles that Leibnitz uses will still
being used centuries later in various machines using the principle of
a stepped gear. A construction that has pins mounted on a cylinder that
on their turn moved gears in a preset sequence. Leibnitz is the first
to use an accumulator (memory alike mechanism).

(11b)For those in the neighborhood: a working
model is on display in the Science museum
in London.

Gottfried
Wilhelm von Leibnitz introduces the use of the handle to multiply and
divide to store the results in calculators.

Each turn make the cylinders turn one or part of a revolution.
Deep into the 20th century this principle will be used in calculators. Leibnitz
also wanted to develop a generalized symbolic language and an algebra to
go with his machines, so that:

"the truth of any proposition in any field of
human inquiry could be determined by simple calculation."

This quest was unsuccessful, but he did invent the calculus and devised
and promoted much of modern mathematical notation still in use today. On
the subject of calculation, Leibnitz wrote:

"It is unworthy of excellent men to lose hours like slaves in
the labor of calculation which could safely be relegated to anyone else
if machines were used."

1678

Grillets Napier calculator at Musee des Arts et Metiers

This calculator
contains 7 "Napiers" rollers and is made of wood and parchement by
a watchmaker called Grillet. (6)

1680

Perrault,
conservator of the Louvre, designed an early handheld calculator with carrying
of tens.

This one appears to have been more a curiosity than a commercial calculator.
That was quite normal is this era: the enlightenment and interbellum.
It were the salons in the French kingdom that pushed the success of gadgets
like this. And as a spin off science advanced rapidly too because no longer
scientist were seen as people playing with some childish toys to amuse them
selves. (6)

1685

One of these famous citations:

For it is unworthy of excellent men to lose hours like
slaves in the labour of calculation which would safely be relegated to
anyone else if machines were used.

1685, Gottfried Wilhelm Leibniz.

1687

Isaac Newton (England)
established his laws of kinetics and gravity and published these laws in his
Philosophiae Naturalis Principia this book also became known as: Principia
Mathematica.

This work proved to be one of the fundamental cornerstones on which the western
science would base its progress in and view on the physical world around us.
Newton is the exact opposite of Leibnitz. The latter is a man of the world
and publishes freely on the infinitesimal mathematics, that were developed
by both Newton and Leibnitz independently of each other though. In how far
communications have been established between Newton and Leibnitz will remain
uncertain. Fact was that Newton kept his knowledge close to his chest and
did very secretive about his knowledge in contrast with Leibnitz who published
whenever he could. That made Newton to publish his findings too in a
way, forced by Leibnitz's publications, though even the infinitsimal mathematics
publication itself was not of Newton's own hand.

Integral Arithmetic

Infinitesimal calculation pushed not only the mathematical sciences
ahead, all Beta sciences profited. Without this knowledge various
sciences would have had to struggle for years with questions unanswered,
but that were now answered more easily by this new knowledge. Especially
astronomers made a giant leap ahead. One could say that the world
of astronomy got totally upside downed.

1690

Newton's publication pushed
Christiaan Huygens to publish his work on the theory of light what he had developed
during the last ten years: Traité de la Lumière (Treatise of Light).

This work was of great influence on the theory of light and further development
of the theoretical aspects of light. His work still shines in the excellence
of the mathematical foundations on which he based the theorems used in his
treatise.

1694

G. W. Leibnitz (Germany)
built a machine that beside the basic calculations also could take the
root from a number.

The last three calculations were done by adding or subtracting repeatingly.
A principle that is still used in 20th century calculators.

Thesis: Calculating the square root of a number is a mathematical process.

Definition: The square root of a number is a number that when raised
one or more times with itself gives back the original number.

Leibnitz invents
the binary calculus.

But his method soon gathered dust also because of his absence. Since he sought
refuge with the Emperor of China. In this era most of the people still thought
that the world is flat and maybe because of that people did not travel far:
out of sight out of heart.
But Leibnitz travelled all the way to China which was only known to a very
few people. and so he and his theories were completely forgotten. Leibnitz
was also taking to the theosophical approach for the binary arithmetic in
a way not taken well by many scientists (4) so
he dropped in their view literally from the world.

Mechanical
calculators were improved upon to such a degree that the main principles became
better known and many inventors improved and expanded on machines that were
already on the market. But speaking of a market might be a bit overdone in view
of this era: the machines were few and expensive.

1706

The first to
use p (pronounced as 'pee') with its present meaning
is an Welsh mathematician William Jones when he states 3.14159 andc. = p

Pi has a history that goes way back into the Egyptian and Persian time; and
is mentioned in the Egyptian Rhind papyrus, which
is dated about 1850 BC.

Many mathematicians tried to calculate a polynominal (meaning: some sort
of regularity...) formula for p. But as far as
research goes no such formula is found. See Wikipedia
for a more detailed discussion, and don't forget to click on the link showing
2000
decimals of p.

1709

Poleni
(1683-1761) constructs a clock calculator.

It resembles a clock driven by a system
of weights . This machine is the first multiplier which uses the principal
of driver with a variable number of teeth. (Collection Museo Nazionale
della Scienza e della Tecnica Milano) ." (15) The
original is said to have been destroyed in a rage by Polini himself
because the errors in the carry mechanism drove him mad in a matter
of speaking.

picture courtesy www-history.mcs.st-andrews.ac.ukl

1720

Calculator by Caze - Musee des Arts et Metiers, Paris

Caze developed
a calculator that transported the twelfth's and parts thereof that suited very
well the ancient French monetary system.

The calculator is placed in a leather casing, with rolls that could be moved
by a wooden pin (see bottom of picture). The rolls look like they were made
of paper or parchment.(6)

1726

Jonathan
Swift (England) described a machine that wrote books automatically in: Gulliver's
Travels. A revolutionary idea that even in the 21st century is not yet
fully realized.

1727

Antonius
Braun (Austria) developed the first calculator with the four base calculations:
add - subtract - multiply and divide.

The one shown in the picture was an exquisite example of craftsmanship of
the 18th century handworkers. A machine also had to be esthetically nice to
the eye was a very common thaugth.

Almost Identical
to the above calculator Jacob Leupold designed a
circular machine based on the principles of Leibnitz.

Its principle was to disengage the gear wheel when the required number of
teeth had meshed with the counter.

1728

Falcon (France)
designed the first programmable loom.

He used wooden punched cards tied together with ropes. This was the first
punched card ever. The Intricate figures and patterns woven into the fabric
were related to the positions of the holes in the punched cards. The combinations
of the holes in the cards were the instructions to the loom mechanism. This
is what we now usually call the first program ever. The invention of the punched
card meant the beginning of automation.
Because automation means that a machine can perform a sequence of actions
without interference of a human being. The human limits its actions by starting
the machine. And before a machine could do anything all actions (instructions)
should be laid down in some (physical) form to achieve a preset goal in advance.
In this perspective the set of instructions laid down in the punched cards
can be called a program(5) (see also
Jacquard 1801/5)

Ada Lovelace (UK) will develop
this idea further over a century later.

Herman Hollerith (USA),
again a bit later, also took upon this idea of instruction cards to improve
the speed and simplicity of data entry with his punched cards .
But it is very plausible that Hollerith got his idea independently of Falcon's
invention. That happened with similar inventions realized into practical products
by many independent inventors. Especially in this period of time where communication
is minimal between scientist.

1730

This illustration shows a human calculator in Japan.

In Japan these calculators were in very high esteem and people went
to professional calculators as to scribents to have them make a calculation
or write business oriented papers such as contracts or inventory lists.
Not until the late 1950's these human calculators rapidly diminished
in "numbers" and the mechanical calculators, like the soroban,
gradually took over their tasks.

Reproduction of a Japanese print from 1730; digitally
reworked by thocf

1760

Benjamin Franklin in Philadelphia (USA) set up lightning rods after
he found out that lightning is a form of electricity.

When he was kiting during a storm and used a key to serve as a conductor
he got literally shocked. His experiments eventually led to the reinvention
of the battery as did the Egyptians centuries before; a primitive battery
was found in a tomb beneath a pyramid. Some years later Volta developed
a somewhat less risky form of electricity and developed a more permanent
battery.

1765

James Watt
(England) invented the steam engine.

This is the engine that started the Industrial Revolution. The steam drove
other machines and made many workers over complete. Opf course this caused
unemployment and thus social unrest. The engines coming forth from this technology
will change the face of the earth within a few decades.

1769

Nearing
the end of the 18th century the advances in watch making technology spurred
rapid developments in mechanics.

One of this advancements drew the attention of the chess loving public. A
machine was created that was said to play chess at a master level. This "machine"
was named "The Turk" causing a sensation when it was exhibited all
across Europe and America for nearly a century. (ref Gary A. Thomas)

The
first chess playing machine ever is invented by the famous Hungarian engineer
and inventor Baron Wolfgang von Kempelen (1734-1804)
who is Counselor on mechanics to the Austrian royal court.

He first exhibits the contraption at the Viennese Royal Palace in 1769. The
Baron claims that the machine can play chess autonomous and winds it up with
a key after which he invited members of the audience to inspect the device
and to play against it. Of course it is a hoax, but no one discovers the secret
until after his death. The automaton is big enough to hide the small person
inside who operates it. After the death of the inventor, the Turk became so
famous that it continues to make world tours. In 1809 at an exhibition in
Shoenbrunn, the Turk plays a famous game against Napoleon 1st. The Turk will
be destroyed in a fire at the museum of Philadelphia in 1856. Other 'chess'
automata will be invented later and continued to perform. Most notably amongst
them are Ajeeb and Mephisto which
work in a similar fashion. (Ref Gary A. Thomas)

1770

In the second
half of the 18-th century this adding machine is created in the city of Nesvige.

The inscription made on this machine, says, that it is invented and made
by “Gevna Jacobson, watchmaker and mechanician in the city Nesvige
in Lithuania, Minsk province ”. The machine is now part of the collection
of scientific tools of the museum Lomonosov in Leningrad.(7)